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The multiplicative factor $q$ assigned to each connected component of a graph in a finite random-cluster measure. At fixed edge probability, the weight of a configuration with $k$ components includes $q^k$. For $q=1$ this reduces to independent bond percolation; increasing $q$ at fixed $p$, for $q\ge 1$, suppresses increasing events by random-cluster weight monotonicity.

The finite-volume random-cluster weight monotonicity passes to consistently wired or free infinite-volume measures for finite increasing connection events. Decreasing these events to origin-to-infinity connectivity yields $\theta (p,q_1)\ge \theta (p,q_2)$ for $q_1\le q_2$. The corresponding supercritical parameter sets are nested, and hence $p_c(q_1)\le p_c(q_2)$.